Downhole positioning control system with force compensation

ABSTRACT

Methods and systems for controlling the downhole position and velocity of a work string using a downhole position and velocity controller may be configured or otherwise programmed to account for force compensation. For example, the work string may undergo significant length changes like thermal expansion and elongation or contraction due to inertial forces, self-weight, and wellbore pressure. Also, the downhole conditions (e.g., temperature, internal forces, self-weight, and wellbore pressure) can cause the work string to be overloaded and become damaged if fast or sudden manipulations occur. The dynamic model implemented with the downhole position and velocity controller may be configured to account for the downhole forces experienced by the work string due to downhole conditions to provide the position and velocity movements that should occur at the surface to achieve the desired position and velocity movements downhole.

BACKGROUND

The present application relates to methods and systems for controllingthe downhole position and velocity of a work string.

In oil and gas well operations, long strings of tubulars (e.g., pipesand coiled tubing), referred to as work strings, are inserted into andremoved from wells at various times. When work strings composed of pipesare inserted into a well, a pipe is attached to the top of a workstring, and then the work string is lowered into the well. When workstrings composed of pipes are removed from a well, a tubular is removedfrom the top of a work string, then the work string is raised from thewell. Depending on the depth of a well, a work string may be thousandsof feet long.

In some instances, dual-jacking systems are used to manipulate the workstring in and out of the wellbore under automated control. That is, insome instances, the position and velocity associated with moving thework string uphole or downhole along the wellbore to insert or removethe work string is automatically controlled by the dual-jacking system.Conventional dual-jacking systems are concerned with the position andmovement of the work string at the surface where the work string entersor exits the wellbore and assumes the same occurs downhole with nochange to the work string length.

BRIEF DESCRIPTION OF THE DRAWINGS

The following figures are included to illustrate certain aspects of theembodiments, and should not be viewed as exclusive embodiments. Thesubject matter disclosed is capable of considerable modifications,alterations, combinations, and equivalents in form and function, as willoccur to those skilled in the art and having the benefit of thisdisclosure.

FIG. 1 is a diagram of a well system implementing a downhole positionand velocity controller.

FIG. 2A is an exemplary computational architecture of a downholeposition and velocity controller coupled to a work string controller.

FIG. 2B pictorially illustrates how the dynamic model approximates thework string as a set of interconnected point lumped masses.

FIG. 2C pictorially illustrates how the dynamic model mathematicallyapproximates the work string as a set of interconnected point lumpedmasses.

DETAILED DESCRIPTION

The present application relates to methods and systems for controllingthe downhole position and velocity of a work string using a downholeposition and velocity controller that accounts for force compensation.

In some instances, the work string may undergo significant lengthchanges like thermal expansion and elongation or contraction due toinertial forces, self-weight, and wellbore pressure. Also, the downholeconditions (e.g., temperature, internal forces, self-weight, andwellbore pressure) can cause the work string to be overloaded and becomedamaged if fast or sudden manipulations occur. The dynamic modelimplemented with the downhole position and velocity controller of thepresent disclosure accounts for the downhole forces experienced by thework string due to downhole conditions to provide the position andvelocity movements that should occur at the surface to achieve thedesired position and velocity movements downhole.

FIG. 1 is a diagram of a well system 100 implementing a downholeposition and velocity controller of the present disclosure. Asillustrated, the well system 100 may include a service rig 102 (alsoreferred to as a “derrick”) that is positioned on the earth's surface104 and extends over and around a wellbore 106 that penetrates asubterranean formation 108. The service rig 102 may be a drilling rig, acompletion rig, a workover rig, or the like. In some embodiments, theservice rig 102 may be omitted and replaced with a standard surfacewellhead completion or installation, without departing from the scope ofthe disclosure. While the well system 100 is depicted as a land-basedoperation, it will be appreciated that the principles of the presentdisclosure could equally be applied in any sea-based or sub-seaapplication where the service rig 102 may be a floating platform orsub-surface wellhead installation, as generally known in the art.

The wellbore 106 may be drilled into the subterranean formation 108using any suitable drilling technique and may extend in a substantiallyvertical direction away from the earth's surface 104 over a verticalwellbore portion 110. At some point in the wellbore 106, the verticalwellbore portion 110 may deviate from vertical relative to the earth'ssurface 104 and transition into a substantially horizontal wellboreportion 112, although such deviation is not required. That is, thewellbore 106 may be vertical, horizontal, or deviated, without departingfrom the scope of the present disclosure. In some embodiments, thewellbore 106 may be completed by cementing a string of casing 114 withinthe wellbore 106 along all or a portion thereof. As used herein, theterm “casing” refers not only to casing as generally known in the art,but also to borehole liner, which comprises tubular sections coupled endto end but not extending to a surface location. In other embodiments,however, the string of casing 114 may be omitted from all or a portionof the wellbore 106 and the principles of the present disclosure mayequally apply to an “open-hole” environment.

The well system 100 may further include a tool 116 that may be conveyedinto the wellbore 106 on a work string 118 (also referred to as a“conveyance”) that extends from the service rig 102. The work string 118may be, but is not limited to, wireline, coiled tubing, drill pipe,production tubing, slickline, electric line, or the like. The workstring 118 is coupled to a positioning tool 120 (e.g., a dual-jack) forautomated control of the velocity and position movement of the workstring 118. The positioning tool 120 is communicably coupled (wired orwirelessly) a positioning tool controller 122 that provides signals thatoperate the positioning tool 120. The positioning tool controller 122includes a downhole position and velocity controller of the presentdisclosure described further in FIGS. 2A-2C.

The well system 100 may include surface sensors 124 that measure surfaceconditions (e.g., a work string condition, a wellbore pressure, a0wellbore temperature, and the like) at or near (e.g., within 100 feet)of the surface 104 (which in an off-shore implementation would be at ornear the surface of the seabed). The surface sensors 124 may bepositioned in a variety of locations. For example, surface sensor 124 ais coupled to the work string 118 at the surface 104, surface sensor 124b is coupled to a portion of the service rig 102, and surface sensor 124c is coupled to the work string 118 near the surface 104. In someinstances, a well system 100 may include one or more sensors that arepositioned within the well system 100 as being coupled to the workstring 118 at or near the surface 104, coupled to the casing at or nearthe surface 104, coupled to a portion of the service rig 102, or in acombination of the foregoing locations.

Surface sensor 124 may be used for one or more surface conditions, whichmay include, but are not limited to, a work string condition, a wellborepressure, a wellbore temperature, and any combination thereof.

Exemplary work string conditions may include, but are not limited to,the strain of the work string 118, the torque applied to the work string118, the rotational speed of the work string 118, the accelerationand/or velocity of the work string 118 being introduced into thewellbore, the positon of the work string 118, the force applied to movethe work string 118 0along the wellbore, and the like, and anycombination thereof. Exemplary surface sensors 124 may include, but arenot limited to, strain sensors, acceleration sensors, position sensors,force sensors, pressure sensors, temperature sensors, and the like, andany combination thereof.

The well system 100 may optionally further include downhole sensors 126that measure downhole conditions, which may include, but are not limitedto, the strain of the work string 118, the torque applied to the workstring 118, 0the rotational speed of the work string 118, theacceleration and/or velocity of the work string 118 being introducedinto the wellbore, the positon of the work string 118, the force appliedto move the work string 118 along the wellbore, the temperature of thefluid in the wellbore 106, the pressure of a fluid in the wellbore 106,and the like, and any combination thereof. The downhole sensors 126 maybe positioned in a variety of locations. For example, downhole sensor126 a is coupled to the work string 118, downhole sensor 126 b iscoupled to the casing (or other liner along the wellbore), and downholesensor 126 c is coupled to the tool 116. In some instances, a wellsystem 100 may include one or more sensors that are positioned withinthe well system 100 as being coupled to the work string 118, coupled tothe casing, coupled to a tool that is coupled to the work string 118, orin a combination of the foregoing locations. Exemplary downhole sensors126 may include, but are not limited to, strain sensors, accelerationsensors, position sensors, force sensors, pressure sensors, temperaturesensors, and the like, and any combination thereof.

The surface sensors 124 and downhole sensors 126 may be communicablycoupled (wired or wirelessly) to the positioning tool controller 122 sothat the positioning tool controller 122 receives signals from thesurface sensors 124 and downhole sensors 126 related to the surfacecondition or downhole condition the respective sensor measures.

FIG. 2A is an exemplary computational architecture (i.e., the design ofand interrelationship between the algorithms, modules, components, etc.)of a positioning tool controller (e.g., the positioning tool controller122 of FIG. 1) that comprises a downhole position and velocitycontroller 2000 and a work string controller 202. The downhole positionand velocity controller 200 comprises four subsystems: an observer 204,a force profile estimator 206, a rate planner 208, and a controller 210.These subsystems work together to produce commands for the work stringcontroller 202.

The observer 204 receives well string inputs 212, which may include, butare not limited to mechanical properties of the well string, geometry0of the wellbore, location of the well string (or sections thereof) inthe wellbore, measured surface conditions, measured downhole conditions,and the like, and any combination thereof. The observer 204 alsocontinuously receives a traveling head force command 214 (F*_(TH)) fromthe work string controller 202. The observer 204 utilizes and maintainsor otherwise updates a dynamic model 216 of the work string. As usedherein, the term “traveling head force” refers to the force applied tothe traveling head by the motor.

FIG. 2B-2C, described in more detail below, illustrate oneimplementation of the dynamic model 216. FIG. 2B pictorially illustrateshow the dynamic model 216 approximates the work string 218 as a set ofinterconnected point lumped masses 220 a-220 j.

Referring again to FIG. 2A, the force profile estimator 206 provides theobserver 204 with point friction forces ({circumflex over (F)}_(D)[j])222 associated with the point lumped masses 220 a-220 j of the dynamicmodel 216. The dynamic model 216 of the observer 204 uses the foregoinginputs 212,214,222 to compute a numerical solution procedure for acertain set of differential equations, which produces outputs 224 forthe current estimated position ({circumflex over (Z)}) and estimatedvelocity ({circumflex over (Ż)}) for each of the point lumped masses 220a-220 j. The estimated position and velocity of each of the point lumpedmasses 220 a-220 j is then mapped to the actual position and velocity ofthe work string 218. As the work string 218 is conveyed along thewellbore, the observer 204 may increment (when moving in the downholedirection 226 of FIG. 2B) or decrement (when moving in the upholedirection 228 of FIG. 2B) the number of point lumped masses 220 a-220 jof the dynamic model 216 to maintain optimal accuracy of the positionand velocity estimation outputs 224, or may change the properties of themasses to account for work string length changes.

FIG. 2C pictorially illustrates how the dynamic model 216 mathematicallyapproximates the work string 218 as a set of interconnected point lumpedmasses 220 a-220 j. The subscript j is used to identify the currentpoint lumped mass (e.g., 220 c) of interest for the following equationsof motion, while subscripts j+1, j−1, and so on are used to identify thepoint lumped one position downhole (e.g., 220 d), one position uphole(e.g., 220 b), and so on of the current point lumped mass (e.g., 220 c).Further, the number of overdot accents for a term indicates thederivative order. For example, a single overdot accent (e.g., {dot over(x)}) indicates the first derivative of the term, the double overdotaccent (e.g., {umlaut over (x)}) indicates the second derivative, and soon.

Eq. (1) provides an exemplary equation of motion for the j^(th) mass,which is mass 220 c as illustrated.

m _(j) {umlaut over (x)} _(j) =−b _(j)({dot over (x)}_(j) −{dot over(x)} _(j−1))+b _(j+1)({dot over (x)} _(j+1) −{dot over (x)} _(j))−k_(j)(x _(j) −x _(j−1))+k _(j+1)(x _(j+1) −x _(j))−{circumflex over (F)}_(D) [j]−F _(g) −F _(p) −k _(j) ∝(ΔT _(j))l _(j) +k _(j+1) ∝(ΔT _(j+1))l_(j+1)   (1)

where:

-   -   m_(j) is a mass of the j^(th) section of the work string    -   x_(j) is a displacement distance of the j^(th) section of the        work string measured from a nominal position    -   k_(j) is an axial spring constant of the j^(th) section of the        work string (defined in Eq. (2))    -   b_(j) is an axial damping coefficient of the j^(th) section of        the work string (defined in Eq. (3))    -   {circumflex over (F)}_(D) is a point friction force    -   F_(g) is a force due to gravity (defined in Eq. (4))    -   F_(p) is a force due to pressure difference between the internal        and external of the work string    -   ΔT_(j) is a change in kinetic energy    -   l_(j) is a length of the j^(th) section of the work string

$\begin{matrix}{k_{j} = \frac{{EA}_{j}}{l_{j}}} & (2)\end{matrix}$

where:

-   -   E is a modulus of elasticity of the work string acting as a        spring    -   A_(j) is a unequalized area of the work string acting as a        spring

b _(j)=2ζ√{square root over (k _(j)½(m _(j−1) +m _(j)))}  (3)

where:

-   -   ζ is a damping ratio

F _(g) =gπ(r _(od) ² −r _(id) ²)(ρ_(steet)−ρ_(mud))   (4)

where:

-   -   g is gravitational acceleration    -   r_(od) is an outside radius of the string    -   r_(id) is an inside radius of the string    -   ρ_(steel) is a density of steel (or other material the j^(th)        section of the work string is composed of)    -   ρ_(mud) is a density of the drilling mud

For a 3-mass system as illustrated in FIG. 2C, the velocity (v_(j)) ofthe j^(th) mass 220 c equals the first derivative of the displacement asdefined in Eq. (5), which produces the matrices in Eq. (6).

v_(j)={dot over (x)}_(j)   (5)

$\begin{matrix}{\begin{bmatrix}{\overset{\cdot}{x}}_{1} \\{\overset{\cdot}{v}}_{1} \\{\overset{\cdot}{x}}_{2} \\{\overset{\cdot}{v}}_{2} \\{\overset{\cdot}{x}}_{3} \\{\overset{\cdot}{v}}_{3}\end{bmatrix} = {\begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\\frac{- \left( {k_{1} + k_{2}} \right)}{m_{1}} & \frac{- \left( {b_{1} + b_{2}} \right)}{m_{1}} & \frac{k_{2}}{m_{1}} & \frac{b_{2}}{m_{1}} & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\frac{k_{2}}{m_{2}} & \frac{b_{2}}{m_{2}} & \frac{- \left( {k_{2} + k_{3}} \right)}{m_{2}} & \frac{- \left( {b_{2} + b_{3}} \right)}{m_{2}} & \frac{k_{3}}{m_{2}} & \frac{b_{3}}{m_{2}} \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & \frac{k_{3}}{m_{3}} & \frac{b_{3}}{m_{3}} & \frac{- k_{3}}{m_{3}} & \frac{- b_{3}}{m_{3}}\end{bmatrix}{\quad{\begin{bmatrix}x_{1} \\v_{1} \\x_{2} \\v_{2} \\x_{3} \\v_{3}\end{bmatrix} + {\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\frac{k_{1}}{m_{1}} & \frac{b_{1}}{m_{1}} & \frac{1}{m_{1}} & {- 1} & \frac{1}{m_{1}} & 0 & 0 & \frac{{- k_{1}}\alpha \; l_{1}}{m_{1}} & \frac{{- k_{2}}\alpha \; l_{2}}{m_{1}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & \frac{1}{m_{2}} & {- 1} & 0 & \frac{1}{m_{2}} & 0 & 0 & \frac{{- k_{2}}\alpha \; l_{2}}{m_{2}} & \frac{{- k_{3}}\alpha \; l_{3}}{m_{2}} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & \frac{1}{m_{3}} & {- 1} & 0 & 0 & \frac{1}{m_{3}} & 0 & 0 & \frac{{- k_{3}}\alpha \; l_{3}}{m_{3}}\end{bmatrix}{\quad\begin{bmatrix}Z_{SF} \\Z_{SF} \\F_{pressure} \\{{g\left( {\rho_{steel} - \rho_{mud}} \right)}/\rho_{steel}} \\{{\hat{F}}_{D}\lbrack 1\rbrack} \\{{\hat{F}}_{D}\lbrack 2\rbrack} \\{{\hat{F}}_{D}\lbrack 3\rbrack} \\{\Delta \; T_{1}} \\{\Delta \; T_{2}} \\{\Delta \; T_{3}}\end{bmatrix}}}}}}} & (6)\end{matrix}$

The force exerted by the positioning tool system (F_(TH)) can be relatedto state variables and inputs 212,214,222 by Eq. (7).

$\begin{matrix}{F_{TH} = {\begin{bmatrix}k_{1} & b_{1} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}x_{1} \\v_{1} \\x_{2} \\v_{2} \\x_{3} \\v_{3}\end{bmatrix} = {\begin{bmatrix}{- k_{1}} & {- b_{1}} & 0 & 0 & 0 & 0 & 0 & {k_{1}\alpha \; l_{1}} & 0 & 0\end{bmatrix}\begin{bmatrix}Z_{SF} \\Z_{SF} \\F_{pressure} \\{{g\left( {\rho_{steel} - \rho_{mud}} \right)}/\rho_{steel}} \\{{\hat{F}}_{D}\lbrack 1\rbrack} \\{{\hat{F}}_{D}\lbrack 2\rbrack} \\{{\hat{F}}_{D}\lbrack 3\rbrack} \\{\Delta \; T_{1}} \\{\Delta \; T_{2}} \\{\Delta \; T_{3}}\end{bmatrix}}}}}} & (7)\end{matrix}$

For clarity, each of the foregoing matrices are abbreviated as providedin Table 1, which allows Eqs. (6) and (7) to be condensed to Eqs. (8)and (9).

TABLE 1 A $\quad\begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\\frac{- \left( {k_{1} + k_{2}} \right)}{m_{1}} & \frac{- \left( {b_{1} + b_{2}} \right)}{m_{1}} & \frac{k_{2}}{m_{1}} & \frac{b_{2}}{m_{1}} & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\frac{k_{2}}{m_{2}} & \frac{b_{2}}{m_{2}} & \frac{- \left( {k_{2} + k_{3}} \right)}{m_{2}} & \frac{- \left( {b_{2} + b_{3}} \right)}{m_{2}} & \frac{k_{3}}{m_{2}} & \frac{b_{3}}{m_{2}} \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & \frac{k_{3}}{m_{3}} & \frac{b_{3}}{m_{3}} & \frac{- k_{3}}{m_{3}} & \frac{- b_{3}}{m_{3}}\end{bmatrix}$ B $\quad\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\frac{k_{1}}{m_{1}} & \frac{b_{1}}{m_{1}} & \frac{1}{m_{1}} & {- 1} & \frac{1}{m_{1}} & 0 & 0 & \frac{{- k_{1}}\alpha \; l_{1}}{m_{1}} & \frac{{- k_{2}}\alpha \; l_{2}}{m_{1}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & \frac{1}{m_{2}} & {- 1} & 0 & \frac{1}{m_{2}} & 0 & 0 & \frac{{- k_{2}}\alpha \; l_{2}}{m_{2}} & \frac{{- k_{3}}\alpha \; l_{3}}{m_{2}} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & \frac{1}{m_{3}} & {- 1} & 0 & 0 & \frac{1}{m_{3}} & 0 & 0 & \frac{{- k_{3}}\alpha \; l_{3}}{m_{3}}\end{bmatrix}$ C [k₁ b₁ 0 0 0 0] D [−k₁ −b₁ 0 0 0 0 0 k₁αl₁ 0 0] U$\quad\begin{bmatrix}Z_{SF} \\Z_{SF} \\F_{pressure} \\{{g\left( {\rho_{steel} - \rho_{mud}} \right)}/\rho_{steel}} \\{{\hat{F}}_{D}\lbrack 1\rbrack} \\{{\hat{F}}_{D}\lbrack 2\rbrack} \\{{\hat{F}}_{D}\lbrack 3\rbrack} \\{\Delta \; T_{1}} \\{\Delta \; T_{2}} \\{\Delta \; T_{3}}\end{bmatrix}$ X $\quad\begin{bmatrix}x_{1} \\v_{1} \\x_{2} \\v_{2} \\x_{3} \\v_{3}\end{bmatrix}$

{dot over (X)}=AX+BU   (8)

F _(TH) =CX+DU   (9)

By considering the traveling head force command (F*_(TH)) as themeasured (F_(TH)), it is possible to construct a full state observeraccording to Eq. (10).

{dot over ({circumflex over (X)})}=(A−LC)){circumflex over(X)}+B−LD)U+LF* _(TH)   (10)

where:

-   -   L is a gain matrix, which is chosen so that the estimate        {circumflex over (X)} converges to the actual state X within a        desired amount of drill time

A Kalman filter may be used within the dynamic model 216 to improve therobustness of the observer 204 performance against surface sensor noise,downhole sensor noise (when downhole sensors are implemented), andprocess (or model) noise.

Referring again to FIG. 2A, the force profile estimator 206 receives theoutputs 224 (i.e., the estimated position ({circumflex over (Z)}),estimated velocity ({circumflex over (Ż)}), and the mass (m_(j)) foreach of the point lumped masses 220 a-220 j from Eq. (1) from theobserver 204). The force profile estimator 206, also, receives orotherwise obtains the traveling head distribution force ({circumflexover (F)}_(D)) 230 from the work string controller 202. The forceprofile estimator 206 records the disturbance friction forces and pointfriction forces associated each depth in lowering the work string forthe first time of a certain service job of a particular well. These dataare then used to predict the friction force trend in subsequent travelthrough the same depth. More specifically, the force profile estimator206 estimates the equivalent frictional forces ({circumflex over(F)}_(D)[j]) for each of the point lumped masses 220 a-220 j of thedynamic model 216 using the traveling head distribution force({circumflex over (F)}_(D)) 230 and estimates stresses of the workstring sections represented by the point lumped masses 220 a-220 j (alsoreferred to as the string stress profile ([σ_(j)]) using the outputs 224from the observer 204.

The force profile estimator 206 provides outputs 230 that comprise thestring stress profile ([σ_(j)]) and the predicted disturbance frictionalforce ({hacek over (F)}_(D)) to the rate planner 208 and providesoutputs 222 that comprise the point friction forces ({circumflex over(F)}_(D)[j]) to observer, as described above.

The rate planner 208 receives a discrete sequence of desired downholeposition (Z*_(DH)[k]) and velocity (Z*_(DH)[k]) commands needed for thewellbore operations being performed. The Z*_(DH)[k] and Ż*_(DH)[k]commands are provided by the operators of the well or an associatedcomputer or model. The rate planner 208 then computes the desireddownhole position ({tilde over (Z)}*_(DH)) and the desired downholevelocity ({tilde over (Ż)}*_(DH)) signals to realize the commandedpositions and accelerations without causing the [σ_(j)] to violate thesafe stress levels of the work string. The computed {tilde over(Z)}*_(DH) and {tilde over (Ż)}_(DH) to achieve the commanded positionsare the outputs 232 of the rate planner 208 that are received by thecontroller 210.

The predicted disturbance friction force ({tilde over ({circumflex over(F)})}_(D)) may optionally then be used to smooth the performance of theapplied downhole force to avoid overloading of the work string. Usingthe predicted disturbance force in the work string controller 202 as thefeedforward signal 234 may reduce the stick/slip behavior that causesthe downhole force to fluctuate and lead to early failure. In someinstances, the rate planner 208 may slow down the work string motion ifthe disturbance shows an increasing pattern of stick/slip behavior thatis difficult to control or estimate. The filtered predicted disturbanceforce is added to the observer 204 feedforward as part of the travelinghead force command 214 (F*_(TH)) of work string controller 202.

The controller 210 uses an appropriate control algorithm (such as aproportional-integral-derivative control algorithm) to compute thesurface position (Z*_(SF)) and surface velocity (Ż*_(SF)) required toobtain the desired downhole position ({tilde over (Z)}*_(DH)) andvelocity ({tilde over (Ż)}*_(DH)). The Z*_(SF) and the Ż*_(SF) areoutputs 236 of the downhole position and velocity controller 200 via thecontroller 210 that are received by the work string controller 202.

The work string controller 202 uses the various outputs from thedownhole position and velocity controller 200 (e.g., the Z*_(SF) and theŻ*_(SF) outputs 236 from the controller 210 and the predicteddisturbance friction force ({tilde over ({circumflex over (F)})}_(D))from the rate planner 208) as inputs to control the movement andposition of the work string via a set of surface position commands(Z*_(SF)) and a set of surface velocity commands (Ż*_(SF)) 238 that aretransmitted to the positioning tool controlling the surface motion andforce (e.g., a dual-jack).

FIGS. 2A-2C and the corresponding description provide examples of amethod, a computational architecture, and algorithms for executing theembodiments of the present disclosure. In some instances, otheralgorithms or computational architectures may be used that accounts forforce compensation when determining the surface position ({tilde over(Z)}*_(SF)) and velocity ({tilde over (Ż)}*_(SF)) outputs 236 of thedownhole position and velocity controller 200.

It is recognized that the various embodiments herein directed to controlsystems, computer control, and analyses, including various blocks,modules, elements, components, methods, and algorithms, can beimplemented using computer hardware, software, combinations thereof, andthe like. To illustrate this interchangeability of hardware andsoftware, various illustrative blocks, modules, elements, components,methods and algorithms have been described generally in terms of theirfunctionality. Whether such functionality is implemented as hardware orsoftware will depend upon the particular application and any imposeddesign constraints. For at least this reason, it is to be recognizedthat one of ordinary skill in the art can implement the describedfunctionality in a variety of ways for a particular application.Further, various components and blocks can be arranged in a differentorder or partitioned differently, for example, without departing fromthe scope of the embodiments expressly described.

Computer hardware used to implement the various illustrative blocks,modules, elements, components, methods, and algorithms described hereincan include a processor configured to execute one or more sequences ofinstructions, programming stances, or code stored on a non-transitory,computer-readable medium. The processor can be, for example, a generalpurpose microprocessor, a microcontroller, a digital signal processor,an application specific integrated circuit, a field programmable gatearray, a programmable logic device, a controller, a state machine, agated logic, discrete hardware components, an artificial neural network,or any like suitable entity that can perform calculations or othermanipulations of data. In some embodiments, computer hardware canfurther include elements such as, for example, a memory (e.g., randomaccess memory (RAM), flash memory, read only memory (ROM), programmableread only memory (PROM), erasable programmable read only memory(EPROM)), registers, hard disks, removable disks, CD-ROMS, DVDs, or anyother like suitable storage device or medium.

Executable sequences described herein can be implemented with one ormore sequences of code contained in a memory. In some embodiments, suchcode can be read into the memory from another machine-readable medium.Execution of the sequences of instructions contained in the memory cancause a processor to perform the process steps described herein. One ormore processors in a multi-processing arrangement can also be employedto execute instruction sequences in the memory. In addition, hard-wiredcircuitry can be used in place of or in combination with softwareinstructions to implement various embodiments described herein. Thus,the present embodiments are not limited to any specific combination ofhardware and/or software.

As used herein, a machine-readable medium will refer to any medium thatdirectly or indirectly provides instructions to a processor forexecution. A machine-readable medium can take on many forms including,for example, non-volatile media, volatile media, and transmission media.Non-volatile media can include, for example, optical and magnetic disks.Volatile media can include, for example, dynamic memory. Transmissionmedia can include, for example, coaxial cables, wire, fiber optics, andwires that form a bus. Common forms of machine-readable media caninclude, for example, floppy disks, flexible disks, hard disks, magnetictapes, other like magnetic media, CD-ROMs, DVDs, other like opticalmedia, punch cards, paper tapes and like physical media with patternedholes, RAM, ROM, PROM, EPROM, and flash EPROM.

Embodiments described herein include Embodiment A, Embodiment B,Embodiment C, Embodiment D, and Embodiment E.

Embodiment A is a method comprising: conveying a work string along awellbore penetrating a subterranean formation using a positioning toolthat controls surface motion and force of the work string, thepositioning tool being coupled to a controller; measuring a surfacecondition selected from the group consisting of a work string condition,a wellbore pressure, a wellbore temperature, and any combinationthereof; modeling the well string with a dynamic model with thecontroller using the surface condition and a geometry of the wellbore asinputs of the dynamic model; calculating a desired downhole position({tilde over (Z)}*_(DH)) and a desired downhole velocity ({tilde over(Ż)}*_(DH)) based on the dynamic model; and conveying the work stringwith the positioning tool to a surface position and velocity based onthe {tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH). Optionally,Embodiment A may further include one or more of the following: Element1: wherein the positioning tool is a dual-jack; Element 2: wherein thework string condition is selected from the group consisting of strain ofthe work string, torque applied to the work string, rotational speed ofthe work string, acceleration of the work string being conveyed into thewellbore, velocity of the work string being conveyed into the wellbore,positon of the work string, force applied to move the work string alongthe wellbore, and any combination thereof; Element 3: the method furthercomprising: measuring a downhole condition with a downhole sensorlocated within the wellbore, wherein the inputs for the dynamic modelfurther include the downhole condition; Element 4: wherein modeling thewell string with a dynamic model involves estimating the well string asa set of interconnected point lumped masses; Element 5: wherein thecontroller comprises a downhole position and velocity controller and awork string controller, and the method further comprising: calculating atraveling head force command (F*_(TH)) of the positioning tool with thework string controller; wherein calculating the {tilde over (Z)}*_(DH)and the {tilde over (Ż)}*_(DH) is also based on the F*_(TH) and isperformed by the downhole position and velocity controller; calculatinga set of surface position commands (Z*_(SF)) and a set of surfacevelocity commands (Ż*_(SF)) based on the {tilde over (Z)}*_(DH) and the{tilde over (Ż)}*_(DH) with the work string controller; and whereinconveying the work string with the positioning tool is according to theŻ*_(SF) and the Ż*_(SF); Element 6: Element 5 and wherein the downholeposition and velocity controller comprises an observer, a force profileestimator, a rate planner, and a controller, and wherein calculating thedesired downhole position and velocity of the work string as performedby the downhole position and velocity controller comprises: calculatinga current estimated position ({circumflex over (Z)}) and estimatedvelocity ({circumflex over (Ż)}) with the observer based on the set ofinterconnected point lumped masses, the surface condition, and thetraveling head force command; calculating a string stress profile([σ_(j)]) and a predicted disturbance frictional force ({hacek over(F)}_(D)) for the work string with the force profile estimator based onthe {circumflex over (Z)} and the {circumflex over (Ż)}; calculating the{tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH) for the workstring with the rate planner based on the [σ_(j)] and the {hacek over(F)}_(D); calculating a surface position (Z*_(SF)) and a surfacevelocity (Ż*_(SF)) of the work string with the controller to produce the{tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH); converting theŻ*_(SF) and the Ż*_(SF) to the set of surface position commands(Z*_(SF)) and the set of surface velocity commands (Ż*_(SF)); Element 7:wherein modeling the well string includes modeling the motion of aj^(th) section of the well string according to Eq. (1); and Element 8:wherein the dynamic model employs a Kalman filter. Exemplarycombinations may include, but are not limited to, two or more ofElements 1-4 in combination; one or more of Elements 1-4 in combinationwith Element 5 and optionally Element 6; one or more of Elements 1-4 incombination with Element 7; one or more of Elements 1-4 in combinationwith Element 8; Element 8 in combination with Element 5 and optionallyElement 6; Element 8 in combination with Element 7; and two or more ofElements 5-8 in combination.

Embodiment B is a well system comprising: a work string extending into awellbore penetrating subterranean formation; a positioning tool coupledto the work string at a surface location of the well system; a surfacesensor that measures a surface condition selected from the groupconsisting of a work string condition, a wellbore pressure, a wellboretemperature, and any combination thereof; a controller communicablycoupled to the positioning tool and the surface sensor, wherein thecontroller includes a non-transitory, tangible, computer-readablestorage medium: containing a program of instructions that cause acomputer system running the program of instructions to: performEmbodiment A optionally with one or more of Elements 1-8.

Embodiment C is a non-transitory, tangible, computer-readable storagemedium: containing a program of instructions that cause a computersystem running the program of instructions to: perform Embodiment Aoptionally with one or more of Elements 1-8.

Embodiment D is a well system comprising: a work string extending into awellbore penetrating subterranean formation; a positioning tool coupledto the work string at a surface location of the well system; a surfacesensor that measures a surface condition selected from the groupconsisting of a work string condition, a wellbore pressure, a wellboretemperature, and any combination thereof; a controller communicablycoupled to the positioning tool and the surface sensor, wherein thecontroller includes a non-transitory, tangible, computer-readablestorage medium: containing a program of instructions that cause acomputer system running the program of instructions to: model the wellstring with a dynamic model with the controller using the surfacecondition and a geometry of the wellbore as inputs of the dynamic model;calculate a desired downhole position ({tilde over (Z)}*_(DH)) and adesired downhole velocity ({tilde over (Ż)}*_(DH)) based on the dynamicmodel; and convey the work string with the positioning tool to a surfaceposition and velocity based on the {tilde over (Z)}*_(DH) and the {tildeover (Ż)}*_(DH).

Embodiment E is a non-transitory, tangible, computer-readable storagemedium: containing a program of instructions that cause a computersystem running the program of instructions to: model a well string witha dynamic model with a controller using a surface condition and ageometry of a wellbore as inputs of the dynamic model; calculate adesired downhole position ({tilde over (Z)}*_(DH)) and a desireddownhole velocity ({tilde over (Ż)}*_(DH)) based on the dynamic model;and convey the work string with the positioning tool to a surfaceposition and velocity based on the {tilde over (Z)}*_(DH) and the {tildeover (Ż)}*_(DH).

Embodiments D and E may optionally include one or more of the following:Element 9: wherein the positioning tool is a dual-jack; Element 10:wherein the work string condition is selected from the group consistingof strain of the work string, torque applied to the work string,rotational speed of the work string, acceleration of the work stringbeing conveyed into the wellbore, velocity of the work string beingconveyed into the wellbore, positon of the work string, force applied tomove the work string along the wellbore, and any combination thereof;Element 11: wherein the controller comprises a downhole position andvelocity controller and a work string controller, and the program ofinstructions that further cause a computer system running the program ofinstructions to: calculate a traveling head force command (F*_(TH)) ofthe positioning tool with the work string controller; wherein theinstruction to calculate the {tilde over (Z)}*_(DH) and the {tilde over(Ż)}*_(DH) is also based on the F*_(TH) and is performed by the downholeposition and velocity controller; calculate a set of surface positioncommands (Z*_(SF)) and a set of surface velocity commands (Ż*_(SF))based on the {tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH) withthe work string controller; and the instruction to convey the workstring with the positioning tool is according to the Ż*_(SF) and theŻ*_(SF); Element 12: Element 11 and wherein the downhole position andvelocity controller comprises an observer, a force profile estimator, arate planner, and a controller, and wherein the instruction to calculatethe desired downhole position and velocity of the work string asperformed by the downhole position and velocity controller includes:calculate a current estimated position ({circumflex over (Z)}) andestimated velocity ({circumflex over (Ż)}) with the observer based onthe set of interconnected point lumped masses, the surface condition,and the traveling head force command; calculate a string stress profile([σ_(j)]) and a predicted disturbance frictional force ({hacek over(F)}_(D)) for the work string with the force profile estimator based onthe {circumflex over (Z)} and the {circumflex over (Ż)}; calculate the{tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH) for the workstring with the rate planner based on the [σ_(j)] and the {hacek over(F)}_(D); calculate a surface position (Z*_(SF)) and a surface velocity(Ż*_(SF)) of the work string with the controller to produce the {tildeover (Z)}*_(DH) and the {tilde over (Ż)}*_(DH); and convert the Ż*_(SF)and the Ż*_(SF) to the set of surface position commands (Z*_(SF)) andthe set of surface velocity commands (Ż*_(SF)); Element 13: wherein theinstruction to model the well string with the dynamic model as a set ofinterconnected point lumped masses accounting for downhole forcesincludes instructions to model the motion of a j^(th) section of thewell string according to Eq. (1); and Element 14: wherein theinstruction to dynamically model the well string as a set ofinterconnected point lumped masses accounting for downhole forcesemploys a Kalman filter. Exemplary combinations may include, but are notlimited to, Elements 9 and 10 in combination; one or both of Elements 9and 10 in combination with Element 11 and optionally Element 12; one orboth of Elements 9 and 10 in combination with Element 13; one or both ofElements 9 and 10 in combination with Element 14; and two or more ofElements 11-14 in combination.

Unless otherwise indicated, all numbers expressing quantities ofingredients, properties such as molecular weight, reaction conditions,and so forth used in the present specification and associated claims areto be understood as being modified in all instances by the term “about.”Accordingly, unless indicated to the contrary, the numerical parametersset forth in the following specification and attached claims areapproximations that may vary depending upon the desired propertiessought to be obtained by the embodiments of the present invention. Atthe very least, and not as an attempt to limit the application of thedoctrine of equivalents to the scope of the claim, each numericalparameter should at least be construed in light of the number ofreported significant digits and by applying ordinary roundingtechniques.

One or more illustrative embodiments incorporating the inventionembodiments disclosed herein are presented herein. Not all features of aphysical implementation are described or shown in this application forthe sake of clarity. It is understood that in the development of aphysical embodiment incorporating the embodiments of the presentinvention, numerous implementation-specific decisions must be made toachieve the developer's goals, such as compliance with system-related,business-related, government-related and other constraints, which varyby implementation and from time to time. While a developer's effortsmight be time-consuming, such efforts would be, nevertheless, a routineundertaking for those of ordinary skill in the art and having benefit ofthis disclosure.

While compositions and methods are described herein in terms of“comprising” various components or steps, the compositions and methodscan also “consist essentially of” or “consist of” the various componentsand steps.

Therefore, the present invention is well adapted to attain the ends andadvantages mentioned as well as those that are inherent therein. Theparticular embodiments disclosed above are illustrative only, as thepresent invention may be modified and practiced in different butequivalent manners apparent to those skilled in the art having thebenefit of the teachings herein. Furthermore, no limitations areintended to the details of construction or design herein shown, otherthan as described in the claims below. It is therefore evident that theparticular illustrative embodiments disclosed above may be altered,combined, or modified and all such variations are considered within thescope and spirit of the present invention. The invention illustrativelydisclosed herein suitably may be practiced in the absence of any elementthat is not specifically disclosed herein and/or any optional elementdisclosed herein. While compositions and methods are described in termsof “comprising,” “containing,” or “including” various components orsteps, the compositions and methods can also “consist essentially of” or“consist of” the various components and steps. All numbers and rangesdisclosed above may vary by some amount. Whenever a numerical range witha lower limit and an upper limit is disclosed, any number and anyincluded range falling within the range is specifically disclosed. Inparticular, every range of values (of the form, “from about a to aboutb,” or, equivalently, “from approximately a to b,” or, equivalently,“from approximately a-b”) disclosed herein is to be understood to setforth every number and range encompassed within the broader range ofvalues. Also, the terms in the claims have their plain, ordinary meaningunless otherwise explicitly and clearly defined by the patentee.Moreover, the indefinite articles “a” or “an,” as used in the claims,are defined herein to mean one or more than one of the element that itintroduces.

The invention claimed is:
 1. A method comprising: conveying a workstring along a wellbore penetrating a subterranean formation using apositioning tool that controls surface motion and force of the workstring, the positioning tool being coupled to a controller; measuring asurface condition selected from the group consisting of a work stringcondition, a wellbore pressure, a wellbore temperature, and anycombination thereof; modeling the well string with a dynamic model withthe controller using the surface condition and a geometry of thewellbore as inputs of the dynamic model; calculating a desired downholeposition ({tilde over (Z)}*_(DH)) and a desired downhole velocity({tilde over (Ż)}_(DH)) based on the dynamic model; and conveying thework string with the positioning tool to a surface position and velocitybased on the {tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH.) 2.The method of claim 1, wherein the positioning tool is a dual-jack. 3.The method of claim 1, wherein the work string condition is selectedfrom the group consisting of strain of the work string, torque appliedto the work string, rotational speed of the work string, acceleration ofthe work string being conveyed into the wellbore, velocity of the workstring being conveyed into the wellbore, positon of the work string,force applied to move the work string along the wellbore, and anycombination thereof.
 4. The method of claim 1 further comprising:measuring a downhole condition with a downhole sensor located within thewellbore, wherein the inputs for the dynamic model further include thedownhole condition.
 5. The method of claim 1, wherein modeling the wellstring with a dynamic model involves estimating the well string as a setof interconnected point lumped masses.
 6. The method of claim 1, whereinthe controller comprises a downhole position and velocity controller anda work string controller, and the method further comprising: calculatinga traveling head force command (F*_(TH)) of the positioning tool withthe work string controller; wherein calculating the {tilde over(Z)}*_(DH) and the {tilde over (Ż)}*_(DH) is also based on the F*_(TH)and is performed by the downhole position and velocity controller;calculating a set of surface position commands (Z*_(SF)) and a set ofsurface velocity commands (Ż*_(SF)) based on the {tilde over (Z)}*_(DH)and the {tilde over (Ż)}*_(DH) with the work string controller; andwherein conveying the work string with the positioning tool is accordingto the Ż*_(SF) and the Ż*_(SF).
 7. The method of claim 6, wherein thedownhole position and velocity controller comprises an observer, a forceprofile estimator, a rate planner, and a controller, and whereincalculating the desired downhole position and velocity of the workstring as performed by the downhole position and velocity controllercomprises: calculating a current estimated position ({circumflex over(Z)}) and estimated velocity ({circumflex over (Ż)}) with the observerbased on the set of interconnected point lumped masses, the surfacecondition, and the traveling head force command; calculating a stringstress profile ([σ_(j)]) and a predicted disturbance frictional force({hacek over (F)}_(D)) for the work string with the force profileestimator based on the {circumflex over (Z)} and the {circumflex over(Ż)}; calculating the {tilde over (Z)}*_(DH) and the {tilde over(Ż)}*_(DH) for the work string with the rate planner based on the[σ_(j)] and the {hacek over (F)}_(D); calculating a surface position(Z*_(SF)) and a surface velocity (Ż*_(SF)) of the work string with thecontroller to produce the {tilde over (Z)}*_(DH) and the {tilde over(Ż)}*_(DH); converting the Ż*_(SF) and the Ż*_(SF) to the set of surfaceposition commands (Z*_(SF)) and the set of surface velocity commands(Ż*_(SF)).
 8. The method of claim 1, wherein modeling the well stringincludes modeling the motion of a j^(th) section of the well stringaccording to Eq. (1):m _(j) {umlaut over (x)} _(j) =−b _(j) ({dot over (x)} _(j) −{dot over(x)} _(j−1))+b _(j+1) ({dot over (x)} _(j+1) −{dot over (x)} _(j))−k_(j) (x _(j) −x _(j−1))+k _(j+1) (x _(j+1) −x _(j))−{circumflex over(F)} _(D) [j]−F _(g) F _(p) m−k _(j)∝(ΔT _(j))l _(j) +k _(j+1)∝(ΔT_(j+1))l _(j+1)   (1) where: m_(j) is a mass of the j^(th) section ofthe work string x_(j) is a displacement distance of the j^(th) sectionof the work string measured from a nominal position k_(j) is an axialspring constant of the j^(th) section of the work string b_(j) is anaxial damping coefficient of the j^(th) section of the work string{circumflex over (F)}_(D) is a point friction force F_(g) is a force dueto gravity F_(p) is a force due to pressure difference between theinternal and external of the work string ΔT_(j) is a change in kineticenergy l_(j) is a length of the j^(th) section of the work string. 9.The method of claim 1, wherein the dynamic model employs a Kalmanfilter.
 10. A well system comprising: a work string extending into awellbore penetrating subterranean formation; a positioning tool coupledto the work string at a surface location of the well system; a surfacesensor that measures a surface condition selected from the groupconsisting of a work string condition, a wellbore pressure, a wellboretemperature, and any combination thereof; a controller communicablycoupled to the positioning tool and the surface sensor, wherein thecontroller includes a non-transitory, tangible, computer-readablestorage medium: containing a program of instructions that cause acomputer system running the program of instructions to: model the wellstring with a dynamic model with the controller using the surfacecondition and a geometry of the wellbore as inputs of the dynamic model;calculate a desired downhole position ({tilde over (Z)}_(DH)) and adesired downhole velocity ({tilde over (Ż)}*_(DH)) based on the dynamicmodel; and convey the work string with the positioning tool to a surfaceposition and velocity based on the {tilde over (Z)}*_(DH) and the{circumflex over (Ż)}_(DH).
 11. The well system of claim 10, wherein thepositioning tool is a dual-jack.
 12. The well system of claim 10,wherein the work string condition is selected from the group consistingof strain of the work string, torque applied to the work string,rotational speed of the work string, acceleration of the work stringbeing conveyed into the wellbore, velocity of the work string beingconveyed into the wellbore, positon of the work string, force applied tomove the work string along the wellbore, and any combination thereof.13. The well system of claim 10, wherein the controller comprises adownhole position and velocity controller and a work string controller,and the program of instructions that further cause a computer systemrunning the program of instructions to: calculate a traveling head forcecommand (F*_(TH)) of the positioning tool with the work stringcontroller; wherein the instruction to calculate the {tilde over(Z)}*_(DH) and the {tilde over (Ż)}*_(DH) is also based on the F*_(TH)and is performed by the downhole position and velocity controller;calculate a set of surface position commands (Z*_(SF)) and a set ofsurface velocity commands (Ż*_(SF)) based on the {tilde over (Z)}*_(DH)and the {tilde over (Ż)}*_(DH) with the work string controller; and theinstruction to convey the work string with the positioning tool isaccording to the Ż*_(SF) and the Ż*_(SF).
 14. The well system of claim13, wherein the downhole position and velocity controller comprises anobserver, a force profile estimator, a rate planner, and a controller,and wherein the instruction to calculate the desired downhole positionand velocity of the work string as performed by the downhole positionand velocity controller includes: calculate a current estimated position({circumflex over (Z)}) and estimated velocity ({circumflex over (Ż)})with the observer based on the set of interconnected point lumpedmasses, the surface condition, and the traveling head force command;calculate a string stress profile ([σ_(j)]) and a predicted disturbancefrictional force ({hacek over (F)}_(D)) for the work string with theforce profile estimator based on the {circumflex over (Z)} and the{circumflex over (Ż)}; calculate the {tilde over (Z)}*_(DH) and the{tilde over (Ż)}*_(DH) for the work string with the rate planner basedon the [σ_(j)] and the {hacek over (F)}_(D); calculate a surfaceposition (Z*_(SF)) and a surface velocity (Ż*_(SF)) of the work stringwith the controller to produce the {tilde over (Z)}*_(DH) and the {tildeover (Ż)}*_(DH); and convert the Ż*_(SF) and the Ż*_(SF) to the set ofsurface position commands (Z*_(SF)) and the set of surface velocitycommands (Ż*_(SF)).
 15. The well system of claim 10, wherein theinstruction to model the well string with the dynamic model as a set ofinterconnected point lumped masses accounting for downhole forcesincludes instructions to model the motion of a j^(th) section of thewell string according to Eq. (1):m _(j) {umlaut over (x)} _(j) =−b _(j)({dot over (x)}_(j) −{dot over(x)} _(j−1))+b _(j+1) ({dot over (x)} _(j+1) −{dot over (x)} _(j))−k_(j) (x _(j) −x _(j−1))+k _(j+1) (x _(j+1) −x _(j))−{circumflex over(F)} _(D) [j]−F _(g) −F _(p) −k _(j)∝(ΔT _(j))l _(j) +k _(J+1)∝(ΔT_(j+1))l _(j+1)   (1) where: m_(j) is a mass of the j^(th) section ofthe work string x_(j) is a displacement distance of the j^(th) sectionof the work string measured from a nominal position k_(j) is an axialspring constant of the j^(th) section of the work string b_(j) is anaxial damping coefficient of the j^(th) section of the work string{circumflex over (F)}_(D) is a point friction force F_(g) is a force dueto gravity F_(p) is a force due to pressure difference between theinternal and external of the work string ΔT_(j) is a change in kineticenergy l_(j) is a length of the j^(th) section of the work string. 16.The well system of claim 10, wherein the instruction to dynamicallymodel the well string as a set of interconnected point lumped massesaccounting for downhole forces employs a Kalman filter.
 17. Anon-transitory, tangible, computer-readable storage medium: containing aprogram of instructions that cause a computer system running the programof instructions to: model a well string with a dynamic model with acontroller using a surface condition and a geometry of a wellbore asinputs of the dynamic model; calculate a desired downhole position({tilde over (Z)}*_(DH)) and a desired downhole velocity ({tilde over(Ż)}*_(DH)) based on the dynamic model; and convey the work string withthe positioning tool to a surface position and velocity based on the{tilde over (Z)}*_(DH) and the {tilde over (Ż)}*_(DH).